A note on the Levenberg-Marquardt parameter

Applied Mathematics and Computation

Volumn 207, Issue 2, 2009, Pages 351-359

  Fan, Jinyan ^a   Pan, Jianyu ^b  

^a SHANGHAI JIAO TONG UNIVERSITY   (China)

^b EAST CHINA NORMAL UNIVERSITY   (China)

Author keywords

Levenberg Marquardt method; Nonlinear equations; Quadratic convergence

Indexed keywords

FUNCTIONS; LAGRANGE MULTIPLIERS;

LEVENBERG-MARQUARDT METHOD; LOCAL ERRORS; NON SINGULARITIES; QUADRATIC CONVERGENCE; RESIDUAL FUNCTIONS;

NONLINEAR EQUATIONS;

EID: 58349084113     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2008.10.056     Document Type: Article

References (18)

1. Levenberg K. A method for the solution of certain nonlinear problems in least squares. Quart. Appl. Math. 2 (1944) 164-166
2. Marquardt D.W. An algorithm for least-squares estimation of nonlinear inequalities. SIAM J. Appl. Math. 11 (1963) 431-441
3. Dennis J.E., and Schnabel R.B. Numerical methods for unconstrained optimization and nonlinear equations. Prentice Hall Series in Computational Mathematics (1983), Prentice Hall Inc., Englewood Cliffs, NJ
4. Yamashita N., and Fukushima M. On the rate of convergence of the Levenberg-Marquardt method. Computing 15 Suppl. (2001) 237-249
5. Fan J.Y., and Yuan Y.X. On the quadratic convergence of the Levenberg-Marquardt method without nonsingularity assumption. Computing 74 (2005) 23-39
6. Ma C., and Jiang L. Some research on Levenberg-Marquardt method for the nonlinear equations. Appl. Math. Comput. 184 (2007) 1032-1040
7. Ma C., Tang J., and Chen X. A globally convergent Levenberg-Marquardt method for solving nonlinear complementarity problem. Appl. Math. Comput. 192 (2007) 370-381
8. Ma C., and Tang J. The quadratic convergence of a smoothing Levenberg-Marquardt method for nonlinear complementarity problem. Appl. Math. Comput. 197 (2008) 566-581
9. Fan J.Y. A modified Levenberg-Marquardt algorithm for singular system of nonlinear equations. J. Comput. Math. 21 (2003) 625-636
10. Moré J.J. The Levenberg-Marquardt algorithm: implementation and theory. In: Watson G.A. (Ed). Lecture Notes in Mathematics 630: Numerical Analysis (1978), Springer-Verlag, Berlin 105-116
11. Moré J.J. Recent developments in algorithms and software for trust region methods. In: Bachem A., Grötschel M., and Korte B. (Eds). Mathematical Programming: The State of Art (1983), Springer, Berlin 258-287
12. Yuan Y.X. Trust region algorithms for nonlinear equations. Information 1 (1998) 7-20
13. Y.X. Yuan, A review of trust region algorithms for optimization, in: J.M. Ball, J.C.R. Hunt (Eds.), ICM99: Proceedings of the Fourth International Congress on Industrial and Applied Mathematics, Oxford University Press, 2000, pp. 271-282.
14. Powell M.J.D. Convergence properties of a class of minimization algorithms. In: Mangasarian O.L., Meyer R.R., and Robinson S.M. (Eds). Nonlinear Programming vol. 2 (1975), Academic Press, New York 1-27
15. Stewart G.W., and Sun J.G. Matrix Perturbation Theory (1990), Academic Press, San Diego, CA
16. Moré J.J., Garbow B.S., and Hillstrom K.H. Testing unconstrained optimization software. ACM Trans. Math. Softw. 7 (1981) 17-41
17. Schnabel R.B., and Frank P.D. Tensor methods for nonlinear equations. SIAM J. Numer. Anal. 21 (1984) 815-843
18. Fan J.Y., and Pan J.Y. Convergence properties of a self-adaptive Levenberg-Marquardt algorithm under local error bound condition. Comput. Optim. Appl. 34 (2006) 47-62